| Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 11, Iss. 3, Jul, 2007, pp. 367-395 @2007 Society for Chaos Theory in Psychology & Life Sciences Delayed Nonlinear Cournot and Bertrand Dynamics with Product Differentiation Abstract: Dynamic duopolies will be examined with product differentiation
and isoelastic price functions. We will first prove that under
realistic conditions the equilibrium is always locally asymptotically
stable. The stability can however be lost if the firms use delayed
information in forming their best responses. Stability conditions are
derived in special cases, and simulation results illustrate the complexity
of the dynamism of the systems. Both price and quantity adjusting models
are discussed. Keywords: delayed dynamics, product differentiation, nonlinear duopoly, limit cycle |